Since the 1960s, numerical control (NC) machining has been the most widely used method to produce mechanical parts. This book describes how to design and implement the mathematical models and algorithms at the core of such CAM/NC machining software systems. Reflecting on nearly two decades of experience in computer-aided manufacturing, the author explains how to design and implement a software system that computes the numerical control programs used to control NC machines. The text presents new experimental approaches in addition to well-known and proven methods. It also provides mathematical models, as well as pseudo code. Topics covered include the Einstein formulation of differential geometry.